David82:
I can already draw 12V, 7A DC through a 6ft length using one twisted pair just fine..
That seems to me about ten times too much current for a CAT5 cable. If you were planning to use RJ45 or similar connectors, I'm sure you'll find they have a very low current rating too.
I think you're also exceeding the rated voltage by about a factor of two.
Bottom line is that this is the wrong cable for the job.
David82:
ignoring the law, can that setup 'technically' work without overheating?
Ignoring the law, it's unsafe. Given that you clearly aren't familiar enough with electrics to understand that for yourself, I recommend that you stick to using cables within their rated capacity and aim to comply with building standards in your area. Not necessarily because it would be necessary for your work to be legal (although that's a good reason) but because it means that you can know that what you're doing is safe.